Answer Happy

4. Let X =   a b c d  . i) Write vec(X); ii) Writevec(X2 )
5. With respect to the previous question, consider F : M(2, R) →M(2, R), F(X) = X2 . Write the form of the corresponding G whichsends vec(X) to vec(X2 ).  Write out the Jacobian matrix of G, atX = A =  α β γ δ  . In other words, write DG(vec(A)).
6. With respect to the previous question write the derivative ofF as a linear map at X = A (no need to derive it, you can use thematerial in the notes). Now write the matrix of this linear mapusing Kronecker products and confirm that it coincides with theJacobian DG(vec(A)) from the previous question.
ONLY DO QUESTION 6 PLEASE
4. Let X = b (ad ad). i) Write vec(X); ii) Write vec(X²). c 5. With respect to the previous question, consider F: M(2, R) → M (2, R), F(X) = X². Write the form of the corresponding G which sends vec(X) to vec(X²). Write out the Jacobian matrix of G, at X = A = αβ 8). In other words, write DG(vec(A)). 7 8 6. With respect to the previous question write the deriva- tive of F as a linear map at X = A (no need to derive it, you can use the material in the notes). Now write the matrix of this linear map using Kronecker prod- ucts and confirm that it coincides with the Jacobian DG(vec(A)) from the previous question.